Sound

• Speech as sound ``Human speech can be described in a simplified way as a stream of acoustic vibrations created by the flow of air through the vocal tract." (Daniloff, p. 3) Just as a clarinet player obtains different notes by using his lips to impart different vibratory modes to the reed and his fingers to open and close a set of holes, so does the human speaker produce the sounds constituting speech by adjusting a number of muscular ``settings" on the speech instrument which is the vocal tract. We need to understand a few things about sound in general before examining the subset of sounds called speech, which are some of the most complex sounds known.
• Definition of sound Albers in ``The World of Sound" defines sound as ``a compressional wave that produces a sensation in the human ear". Notice that according to this definition, human perception is required in order to have sound.
• Sound waves are longitudinal mechanical waves with the following properties:
  • Huygen's principle ``All points on a wave act as sources of circular waves (or spherical waves in three dimensions); the total wave pattern at some later time will be the sum of all the individual Huygen's wavelets."
  • Superposition ``The existence of one wave does not affect the existence of properties of another wave."
  • Inverse square law ``The intensity of a sound wave is inversely proportional to the [distance from the source in two dimensions and] decreases in proportion to the square of the distance from the source [in three dimensions]." (The previous quotes are from Berg and Stork, The Physics of Sound.)
  • Reflection Waves can bounce off a surface like a light wave bounces off a mirror; the reflected angle is equal to the incident angle reflected around the normal to the surface.
  • Refraction The passage from one medium to another is normally accompanied by a change of the wavefront direction.
  • Interference Two similar waves can combine constructively or destructively; musical beats are an example of this behavior.
  • Diffraction Waves can bend around obstacles even in the absence of a change of medium; this behavior arises as a result of Huygen's principle.
• Sound depends on mass and elasticity Many types of physical systems can produce sounds, but in all cases they must be able to vibrate. If a sound source is distant from the listener, there must be some medium of transmission which is also able to vibrate in resonance with the sound source. Vibration is a cyclical transformation of kinetic energy to potential energy and back again. In order that this cycle may be sustained, all vibrations depend on two physical properties: mass and elasticity.
• Sound transmission in air The medium of sound transmission in normal circumstances is the air of the earth's atmosphere. The vibratory activity produced by a sound source gives rise to pressure fluctuations in the air. Pressure is a measure of force per unit area. At sea level, air pressure is approximately 14.7 pounds per square inch, or 100,000 Nt/m or Pascals (Pa). At this pressure, each cubic inch of air contains about 400 billion billion ( ) molecules of air. This is the mass involved in sound transmission in the air. The elasticity of air is the tendency of compressed air to return to its former volume, thus converting the potential energy stored by compression into the kinetic energy of movement.
• Example of the tuning fork The simplest type of sound which we can produce is that exemplified by the tuning fork which produces E above middle C. When we strike such a tuning fork against another solid object, we impart to it a force which results in vibratory motion lasting for several seconds. The tines of the tuning fork move first in one direction, then in the other direction. Notice that this movement, like all vibratory movement, depends upon the mass and the elasticity of the tuning fork.
• Condensation The movement first causes compression or condensation in the air near the tines. This condensation may be defined as an area of increased density compared to that of the overall air mass. The increased density causes increased pressure, and the human ear is sensitive to this increase.
• Rarefaction When the tines move in the opposite direction because of their elasticity, the air's elasticity causes it to return to its former volume. Because of the inertia of the air mass, the mass overshoots and expands even beyond its original volume. Now the density of this portion of air is less than atmospheric pressure. Thus, an area of rarefaction succeeds the area of condensation. The ear is also sensitive to this decrease in pressure.
• Sound is the passage of areas of condensation and rarefaction As the tines continue to vibrate, they impart successive areas of condensation and rarefaction to the air adjacent to the tuning fork. These initial changes in air pressure result in similar variations taking place a little further away from the tuning fork, and a little later in time, because of the action of the air molecules in the originally affected area. Each air molecule moves only an infinitesimal distance before knocking into a neighbor, but sound travels as the propagation of density changes in the air mass as a whole. Sound, then, may be considered as waves of differing air pressure radiating away from the sound source in all directions, which eventually arrive at the eardrums of a human being and thus become perceptible. The waves of air pressures variations are represented in Figure 2a. If we graph the variations in air pressure for a sound wave over time, we have a time-domain waveform, or simply a waveform, of the sound source. A waveform of a tuning fork looks like that in Figure 2b.
• Human hearing is sensitive to a range of pressure variations Remember that resting atmospheric pressure is on the order of 100,000 Pa. The human ear is sensitive to pressure variations as small as 0.00002 Pa. The upper limit of pressure fluctuation which can be tolerated without discomfort or damage is on the order of 20 Pa. Thus there is a range of pressure variations of to which the human ear is sensitive.
• Pressure and Intensity Pressure is defined as force per unit area, and is measured in Newtons/m or Pascals. Intensity is defined as power per unit area and is measured in Watts/m . We have seen that audible pressure variations can range from .00002 Pa to 20 Pa, varying by a factor of . Since intensity is proportional to the square of pressure variation, audible intensities can range from W/m to 1 W/m , a factor of . Instead of comparing intensities directly, therefore, it is more convenient to use a related parameter called the sound level, which is expressed in decibels as follows:

  

  where is often the standard reference intensity ( = 10 W/m ) chosen because it is near the lower limits of audibility. However, any reference intensity level may be used.

• The speed of sound depends on density and elasticity Sound comes to our ears as waves of differing pressure caused by a vibrating sound source and propagated through the air (or some other medium) by the action of billions of molecules striking one another. The speed of sound transmission is determined by two factors:
  • It is directly proportional to the square root of the elasticity of the medium.
  • It is inversely proportional to the square root of the density of the medium.

  Thus an increase in temperature results in an increase in the speed of sound because it reduces the density of the conducting medium. In air at a temperature of C, the speed of sound is 331 m/s; at C, the speed is 343 m/s.

• The speed of sound varies greatly in different media A change in the conducting medium makes a more significant change in the speed of sound than changes in the density of a given medium. In water at , the speed is more than four times as great as in air: 1433 m/s. In a steel rail it is greater still: 4704 m/s. This is because steel is 6000 times denser than air, which would tend to slow the speed of sound transmission down; but 1,230,000 times more elastic, which results in the final ratio of .